Harlequins fly-half Smith picked up the injury at England's training camp in Girona on Monday and has been ruled out of the trip to Rome.
England are waiting for a second opinion on a scan before confirming a potential return date for Smith, raising the possibility that he could miss additional matches.
The 24-year-old had been expected to start against Italians, with George Ford and Fin Smith also competing for the fly-half role.
"He won't make this weekend sadly," England assistant coach Kevin Sinfield told reporters on Tuesday.
"It is a calf injury. We got the scan report through but we are waiting to understand exactly what that means for us moving forward. He's not fit for this weekend.
"It just happened in training, the early part of the session. Just one of those things. The boys have had two days off (for) recovery and Marcus being the bundle of energy that he is was doing his thing.
"Unfortunately, these things happen. We are gutted for him because he's been amazing to work with and we hope it will not be too long."
Prior to his injury setback, Smith was hoping to step out of Owen Farrell's shadow after his rival for the number 10 jersey ruled himself out of the Six Nations for mental wellbeing reasons.
Farrell was first choice in the position at the World Cup, with Smith converted to full-back.
England boss Steve Borthwick will pick his replacement from 91-cap Ford or the uncapped Fin Smith, a 21-year-old who has been in fine form for Northampton this season.
"Marcus is a big loss. He's an outstanding guy who I have absolutely loved working with and I have got a really good connection with," Sinfield said.
"But what that does is provide opportunities for others. We have said it since I have been working with England that we are blessed with the 10s that we have got."
